Improving dimensionality-reduction for carbon-emissions prediction using hybrid quantum annealing-based feature selection and PCA

Accurate carbon-emissions prediction is critical for evidence-based climate policy, where even modest improvements can influence emission–reduction targets. However, high-dimensional datasets often exhibit noise, nonlinear dependencies, and multicollinearity that degrade model stability. We propose QMICO-PCA, a hybrid dimensionality-reduction method that integrates quantum annealing (QA)-based feature selection with principal component analysis (PCA). In the selection stage, mutual information (MI) and Pearson correlation (CO) are combined multiplicatively within a QUBO formulation to jointly reward nonlinear relevance and penalize linear redundancy, enabling balanced subset optimization. The selected features are then transformed via PCA to enhance generalization and mitigate overfitting. We evaluate QMICO-PCA against classical approaches (RFE, LASSO, ELN), with and without PCA, using three regression models on the Our World in Data carbon dataset (13,706 records; 79 features; 1970–2023). Experiments are conducted on heterogeneous QA-based solvers to assess optimization robustness. QMICO-PCA achieves the strongest overall performance (average RMSE = 1134.12, MAE = 237.54, $$R^2$$ = 0.8020), corresponding to a 4-7% error reduction over classical methods. In multi-year emission prediction, such reductions can lead to lower cumulative projection errors, supporting more reliable quantitative policy design. Statistical analysis confirms significance (Friedman $$p=0.0018$$ ) with a strong effect size ( $$W=0.975$$ ) and significant Holm-adjusted post-hoc comparisons ( $$p_{\text {holm}}<0.05$$ ). As additional validation, the proposed method is further evaluated on small-scale carbon-emissions datasets, where it also demonstrates consistent performance. Overall, these findings suggest that the proposed method provides a competitive approach for high-dimensional carbon-emissions modeling.